Tournament-server reports wrong color in pairings (everyone white), so
auto-joined games could play with an inverted color and never move on
their real turn. The game endpoint white/black ids are correct, so the
poll loop now derives our color from it, falling back to the passed-in
color. Both stream and auto-join entry paths are now immune to the bug.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>